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25 September 2022
 
  » arxiv » math.GT/9912050

 Article overview


Knots and links without parallel tangents
Ying-Qing Wu ;
Date 6 Dec 1999
Subject Geometric Topology MSC-class: 57M25 | math.GT
AbstractSteinhaus conjectured that every closed oriented $C^1$-curve has a pair of anti-parallel tangents. Porter disproved the conjecture by showing that there exist curves with no anti-parallel tangents. Colin Adams rised the question of whether there exists a nontrivial knot in $R^3$ which has no parallel or antiparallel tangents. The main result of this paper solves this problem, showing that any (smooth or polygonal) link $L$ in $R^3$ is isotopic to a smooth link $hat L$ which has no parallel or antiparallel tangents.
Source arXiv, math.GT/9912050
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